## Matrix Algebra: LU Decomposition Method

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra. In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra. Here is the seventh topic where we talk about solving a set of simultaneous linear equations using the LU decomposition method.  First, the LU decomposition method is discussed along with its motivation.  The LU decomposition method to find the inverse of a square matrix is discussed. Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation. LU Decomposition Method
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• the Massive Open Online Course (MOOCs) available at

## Matrix Algebra: Gaussian Elimination Method

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra. In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra. Here is the sixth topic where we talk about solving a set of simultaneous linear equations using Gaussian elimination method – both Naive and partial pivoting methods are discussed. How to find determinants by using the forward elimination step of Gaussian elimination is also discussed.  Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation. Gaussian Elimination Method
This post is brought to you by
• Holistic Numerical Methods Open Course Ware:
• the textbooks on
• the Massive Open Online Course (MOOCs) available at

## Matrix Algebra: System of Equations

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra. In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra. Here is the fifth topic where we talk about setting up simultaneous linear equations in matrix form, consistent and inconsistent system of equations, the rank of a matrix, conditions when unique, infinite number or no solutions exist, and finding the inverse of a square matrix.  Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation. System of Equations
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• Holistic Numerical Methods Open Course Ware:
• the textbooks on
• the Massive Open Online Course (MOOCs) available at

## Adaptive learning improves the flipped classroom

A two-year exploratory study conducted at the University of South Florida, and evaluated and assessed by the University of Pittsburgh, studied the effect of using adaptive lessons in improving pre-class learning in a flipped classroom.

Read the whole article here: https://www.smartsparrow.com/demos/numerical-methods/

This material is based upon work supported partially by the National Science Foundation under Grant Number 1609637. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

## Matrix Algebra: Unary Operations

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra. In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra. Here is the fourth topic where we talk about unary operations on a matrix including transpose, symmetry, determinant, and trace of a matrix.  Methods of finding determinants along with some fundamental theorems of determinants are discussed.  Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation. Unary Operations
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• Holistic Numerical Methods Open Course Ware:
• the textbooks on
• the Massive Open Online Course (MOOCs) available at

## Matrix Algebra: Vectors

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra.

In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra.

Here is the second topic where we talk about vectors, binary operations on vectors, set up the concept of linear combination and linear independence of vector.  Learn how vectors are used to set up simultaneous linear equations.  Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation.

Vectors

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## Matrix Algebra: Binary Operations

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra.

In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra.

Here is the third topic where we talk about binary operations of matrices – subtraction, addition, and multiplication.  Linear combination of matrices and rules of binary operations are discussed. Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation.

Binary Operations

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